Doctoral Dissertations


"The objective of this study is to describe in a unified manner a group of structural dynamics analyses using the substructures technique. An additional effort is to provide a consistent basis for the selection of substructure principal modes as required by this method. Substructure principal mode frequency roots and strain energy are two criteria evaluated for the selection of substructure principal modes. System eigenvalues and system strain energy are investigated for the comparison of results in the principal modes. System strain energy should provide more rational results since it is proportional to the stress times the strain in the system and summed over the entire system. Expressions for estimating errors in system eigenvalues and strain energy in the principal modes due to omission of certain substructure principal modes are derived. To complete the solution to the free undamped vibrations problem, the substructures method is extended to include solution with initial conditions. A simple example of a cantilever beam is presented. It is noted through this example that the criterion based on substructure normal mode strain energy for retaining substructure principal modes provides slightly better results in terms of system eigenvalues and strain energy in the principal modes. Estimation of errors in system strain energy in the principal modes due to modal truncation is better in comparison to the estimate of errors in system eigenvalues. The substructures method is also applied to complex structures under forced excitation. Since the classical direct approach results in large order complete structure matrices, computer storage may exceed that which is available on most digital machines. Partitioning of matrices, via the substructures method, is one of the important features of this study and helps keep the computer storage and cost to a minimum. Matrix partitioning is utilized to its fullest extent in deriving equations of motion and in providing their solutions. Several practical excitations are considered through a simple example of a cantilever beam. Approximate solutions for transverse displacements and system strain energy are evaluated for the purpose of comparisons with the 'exact' case when no modal truncation is used. Results show the applicability of the substructures method to systems under forced excitation"--Abstract, pages ii-iii.


Lehnhoff, T. F., 1939-

Committee Member(s)

Cronin, Don
Cunningham, Floyd M.
Sauer, Harry J., Jr., 1935-2008
Penico, Anthony J., 1923-2011
Faucett, T. R.


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Mechanical Engineering


University of Missouri--Rolla

Publication Date



xiv, 186 pages

Note about bibliography

Includes bibliographical references (pages 152-154).


© 1972 Suresh Kumar Tolani, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Vibration -- Mathematical models
Damping (Mechanics)
Structural control (Engineering)

Thesis Number

T 2787

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